- Calculate the difference between the original and final values: \(1,865 - 1,240 = 625\).
- Divide the difference by the original value: \(\frac{625}{1,865} \approx 0.3351\).
- Convert to a percentage: \(0.3351 \times 100\% = 33.51\%\).
- Match the result to the provided options, which corresponds to \(\boxed{b}\).
Explanation
- Calculating the Percent Decrease
The problem asks for the percent decrease from an initial value of \(1,865\) to a final value of \(1,240\). A percent decrease represents how much a quantity has dropped relative to its original amount, expressed as a percentage. The formula for calculating this is:
\[\text{Percent Decrease} = \frac{\text{Original Amount} - \text{Final Amount}}{\text{Original Amount}} \times 100\%\]
We first determine the absolute amount of the decrease by subtracting the final value from the original value:
\[\text{Amount of Decrease} = 1,865 - 1,240 = 625\]
Next, we divide this amount by the original value to find the ratio of the decrease:
\[\text{Ratio} = \frac{625}{1,865} \approx 0.33512\]
Finally, to convert this ratio into a percentage, we multiply by \(100\%\):
\[\text{Percent Decrease} \approx 0.33512 \times 100\% = 33.512\%\]
Comparing this result to the given options:
A\(66.5\%\)
B\(33.5\%\)
C\(50\%\)
D\(150\%\)
The calculated value of approximately \(33.5\%\) matches option (b).
Examples
Percent decrease is widely used in everyday life, such as when items go on sale. If a jacket was originally priced at \$100 and is now \$80, the percent decrease is \(\frac{100-80}{100} \times 100\% = 20\%\). Understanding how to calculate this helps you make informed decisions while shopping, evaluating financial growth, or tracking changes in data over time.